$1.(30$ Points$)$ Refer to Ch$.8($P$377-381)$ and answer the following questions $($please provide details with calculation if it is applicable$)$: $(1)$ Shannon$$s Sampling Theorem states that $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.(2)$ The Nyquist frequency in a signal that has $10$ Hz$,100$ Hz$,$ and $500$ Hz frequency components is: $\_\_\_\_\_\_\_\_\_.(3)$ If the sampling rate is $2\mathrm{.}5$ kHz$,$ the time interval between samples would be $\_\_\_\_\_\_\_\_\_\_\_\_\_.(4)$ Aliasing can result when sample a signal V$($t$)=$ sin$($t$)+$ sin$(2$t$)$ at less than $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.(5)$ An A$/$D converter includes which four basic components? $($refer to the lecture notes$)\_\_\_\_\_\_\_\_\_.(6)$ An analog multiplexer is used to $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.$